Physics – Mathematical Physics
Scientific paper
2002-02-19
in: "Multiple facets of quantization and supersymmetry", Eds. M. Olshanetsky and A. Vainshtein, World Scientific, 2002
Physics
Mathematical Physics
to appear in the "Michael Marinov Memorial Volume"
Scientific paper
Parity is ubiquitous, but not always identified as a simplifying tool for computations. Using parity, having in mind the example of the bosonic/fermionic Fock space, and the framework of Z_2-graded (super) algebra, we clarify relationships between the different definitions of supermanifolds proposed by various people. In addition, we work with four complexes allowing an invariant definition of divergence: - an ascending complex of forms, and a descending complex of densities on real variables - an ascending complex of forms, and descending complex of densities on Grass mann variables. This study is a step towards an invariant definition of integrals of superfunctions defined on supermanifolds leading to an extension to infinite dimensions. An application is given to a construction of supersymmetric Fock spaces.
Bell Maria E.
Cartier Pierre
DeWitt-Morette Cecile
Ihl Matthias
Saemann Christian
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